Hyperuniform disordered material with resonant structures

ABSTRACT

An optical structure includes a Hyperuniform Disordered Solid (“HUDS”) structure, a waveguide, and a resonant cavity. The HUDS structure is formed by walled cells organized in a lattice. The waveguide is configured to guide an optical signal. The resonant cavity is formed along a boundary of the waveguide. The resonant cavity is configured to be resonant at a frequency band that is a subset of a bandwidth of the optical signal.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Applications No.61/949,703 and No. 61/949,717, which were both filed Mar. 7, 2014 andare hereby incorporated by reference.

This application is related to non-provisional applications entitled“Hyperuniform Disordered Structures with Improved Waveguide Boundaries”(U.S. Ser. No. 14/642,494) and “Hyperuniform Disordered Material withPerforated Resonant Structures,” (U.S. Ser. No. 14/642,519) filed Mar.9, 2015 and are hereby incorporated by reference.

TECHNICAL FIELD

This disclosure relates generally to Hyperuniform Disordered Solidstructures, and in particular, but not exclusively to opticalwaveguides.

BACKGROUND INFORMATION

Conventional data networks are bumping up against physical limitationsas the demand for higher bit rates increases. The physical limitationsinclude size, thermal considerations, and transmission speed. Opticalnetworks are becoming increasingly important as they mitigate some ofthe physical limitations of conductively wired (e.g. copper) networks.Highly compact optical waveguides and filters facilitate the high bitrate transmission of information within and between computers.

Conventional planar waveguide systems, typically based on air-clad,oxide-clad, or nitride-clad structures such as rectangular strip, rib,and slot waveguides, support the design, fabrication, and planarintegration of the full set of photonic components required to createphotonic integrated circuits (PICs) for current applications to sensing,communications, and optical networking. The bending radius of suchstructures varies from hundreds of microns for the lowest-losswaveguides to several microns for some of the most tightly-bending, andsubstantially lossier waveguides. These conventional strip, rib, andslot waveguides have been formed into rings, Archimedean spirals, andthe complex waveguide delay patterns increasingly used in chip-scalephotonic implementations of complex optical coding schemes such as DPSK,DQPSK, and OAM (a.k.a. spatial division multiplexing, or vortex wavemultiplexing). These and other complex photonic integrated circuitlayouts have all been demonstrated using conventional planar waveguides.However, waveguide size constraints in conventional PICs limitsreduction of the physical dimensions of the PICs.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments of the invention aredescribed with reference to the following figures, wherein likereference numerals refer to like parts throughout the various viewsunless otherwise specified.

FIG. 1A shows a Hyperuniform Disordered Solid (“HUDS”) structure thatincludes walled cells organized in a lattice.

FIG. 1B shows a zoomed in view of a HUDS structure and a waveguideincluded in FIG. 1A.

FIG. 2A illustrates an example of an optical structure that includeswalled cells organized in a lattice, in accordance with an embodiment ofthe disclosure.

FIG. 2B shows a diagram of a zoomed-in portion of FIG. 2A, in accordancewith an embodiment of the disclosure.

FIG. 2C shows an example structure that includes an optical structure,in accordance with an embodiment of the disclosure.

FIG. 3A illustrates boundaries for HUDS tile designs that can be used togenerate an optical structure, in accordance with an embodiment of thedisclosure.

FIG. 3B illustrates a more complex boundary condition that might beused, for example, to create a particularly compact edge coupler, inaccordance with an embodiment of the disclosure.

FIG. 3C shows a HUDS tile having tile sections, in accordance with anembodiment of the disclosure.

FIG. 4 shows the efficiency of the waveguide from FIG. 2A, in accordancewith an embodiment of the disclosure.

FIGS. 5A-5B illustrates an optical structure including an exampleresonant cavity, in accordance with an embodiment of the disclosure.

FIG. 5C illustrates an optical structure having an example resonantcavity, in accordance with an embodiment of the disclosure.

FIG. 6 illustrates a chart showing the performance of a waveguide in anexample optical structure, in accordance with an embodiment of thedisclosure.

FIGS. 7A-7B illustrates the transmission of optical structures overtemperature ranges, in accordance with an embodiment of the disclosure.

FIGS. 8A and 8B illustrate a HUDS based optical modulator that can beincluded in a photonic integrated circuit (“PIC”), in accordance with anembodiment of the disclosure.

FIGS. 8C and 8D show example resonant structures that can be used as theresonant structure in FIGS. 8A and 8B, in accordance with an embodimentof the disclosure.

FIGS. 8E-8F show plan views of example resonant cavities having firstand second doping regions disposed in a semiconductor lattice to changethe electrical field to modulate an optical signal propagating through awaveguide, in accordance with an embodiment of the disclosure.

FIG. 9 illustrates a block diagram of an example optical transceiver 999that includes a HUDS PIC 980, in accordance with an embodiment of thedisclosure.

FIG. 10 illustrates a schematic of ordering Approaches #1 and #2.Approach #1 indicated by the two “X” marks and triangle labelled “1”, inaccordance with an embodiment of the disclosure.

FIG. 11 illustrates a point distribution of the fixed points for a bendin which the points are arranged according to Approach #1, #2, and #3,respectively, in accordance with an embodiment of the disclosure.

FIG. 12 shows the waveguide modes of a triangular photonic crystal ofhexagons, i.e. a honeycomb structure, in accordance with an embodimentof the disclosure.

FIG. 13 illustrates transmission at successive virtual monitors along along (80a) regular honeycomb waveguide, in accordance with an embodimentof the disclosure.

FIG. 14 illustrates the disordered honeycomb structures with embeddedwaveguides, in accordance with an embodiment of the disclosure.

FIG. 15 shows the spectral transmission as a function of wavelength forour three designs, in accordance with an embodiment of the disclosure.

DETAILED DESCRIPTION

Embodiments of Hyperuniform Disordered (“HUD”) structures and systemsincluding HUD structures are described herein.

In one embodiment of the disclosure, an arbitrarily-shaped waveguide iscreated by using the edges of the waveguide as one of the boundaryconditions for the creation of a hyperuniform point pattern in thevicinity around the waveguide.

In another embodiment of the disclosure, an arbitrarily-shaped waveguideis created by first drawing the desired path of the waveguide through apre-determined HUDS pattern without regard to whether or not the drawnpath aligns with the original features in the HUDS pattern, thenadjusting the HUDS features immediately adjacent to the waveguide so asto restore the hyperuniformly disordered packing pattern along theboundary of the waveguide path. Then, the HUDS points (and theirassociated walls) at the next row away from the boundary are adjusted.

In another embodiment of the disclosure, a HUDS-based photonicintegrated circuit (PIC) forms an optical transmitter. Opticaltransmitters are known to comprise one or more light sources such aslasers, modulators, optional wavelength combiners, and optionalintensity controllers. Each of these components can be made using HUDS,and can advantageously be either monolithically or hybridly integratedonto a single HUDS-based PIC. For the light source in the opticaltransmitter, HUDS can, for example, be designed into a III-V materialsystem to confine light in an LED or laser gain medium, they hybridlyintegrated with another PIC made out of a material other than a III-V,such as silicon. Another way to use HUDS to confine light in an LED orlaser gain medium is to design HUDS into a substrate such as silicon soas to create a high Q resonant cavity in the silicon which isevanescently-coupled to a III-V-based or other optical gain medium.Alternatively, a conventional non-HUDS-based light source can behybridly-coupled into a HUDS-based photonic integrated circuit (PIC) viaany number of coupling techniques known in the art, such as edgecouplers and vertical couplers. A HUDS-based vertical coupler providesimproved angular tolerance over vertical couplers based on periodicstructures. Once coupled into the PIC, a HUDS-based waveguide carriesthe signal to a HUDS-based modulator. HUDS-based modulators can beeither resonant or non-resonant.

In further embodiments of the invention, substantial performanceimprovements can be achieved in the use of HUDS-based photonic band gapstructures to lay out photonic integrated circuits featuring rings,Archimedean spirals, and the complex waveguide delay patternsincreasingly used in chip-scale photonic implementations of complexoptical coding schemes such as DPSK, DQPSK, and OAM (a.k.a. spatialdivision multiplexing, or vortex wave multiplexing).

In the following description, numerous specific details are set forth toprovide a thorough understanding of the embodiments. One skilled in therelevant art will recognize, however, that the techniques describedherein can be practiced without one or more of the specific details, orwith other methods, components, materials, etc. In other instances,well-known structures, materials, or operations are not shown ordescribed in detail to avoid obscuring certain aspects.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the present invention. Thus, theappearances of the phrases “in one embodiment” or “in an embodiment” invarious places throughout this specification are not necessarily allreferring to the same embodiment. Furthermore, the particular features,structures, or characteristics may be combined in any suitable manner inone or more embodiments.

Photonic Band Gap (PBG) solids are artificial dielectric materials usedto “Mold the Flow of Light,” and analogous in some respects to howsemiconductors are used in electronic applications. While PBG solids aremade from common materials such as, for example, silicon and air, theiroptical properties differ substantially from the optical properties ofeither silicon or air, in accordance with the geometric arrangement ofthe silicon and air at a size scale that is small relative to thewavelength of light. For example, a PBG structure can be designed andfabricated to prohibit the flow of light, even though it is made out oftwo materials which are each transparent to light. Such a PBG can beused as an optical insulator or mirror which forces light to remainconfined in waveguides defined by the edges of the PBG material. PBGmaterials are typically a latticework of two interpenetrating substanceswith different indices of refraction (e.g., silicon and air), arrangedin unit cells dimensioned on the order of a half a wavelength of theradiation to be controlled. For certain arrangements of materials, thesolid has a complete PBG, a range of frequencies for whichelectromagnetic wave propagation is prohibited for all directions andpolarizations. A complete PBG (analogous to an electronic band gap in asemiconductor) is the key feature needed for many technologicalapplications, including efficient radiation sources, telecommunicationsdevices (optical fibers and waveguides, T-branches, channel-drops,etc.), sensors, and optical computer chips.

Increasingly complex PBG-based photonic components which have beendesigned, fabricated and tested based on periodic PBG systems includewaveguides, n-way splitters, resonant and non-resonant filters includingsuper-prisms, beam combiners, vertical couplers, LEDs, lasers,modulators, switches, and detectors. Integrated together, thesecomponents have been combined into complex systems or subsystemsincluding but not limited to transmitters, receivers, and sensors.

Periodicity of the sub-wavelength unit cells making up the PBG latticewas long thought to be a requirement for obtaining a photonic band gap.Quasiperiodic lattices designed to have a photonic band gap weresubsequently invented. The layout of waveguides in conventional(periodic) Photonic Crystal (PhC) and Photonic QuasiCrystal (PhQC) PBGmaterials was tightly constrained to follow the PhC and PhQC crystalaxes.

Applications in which compact, energy-efficient, and low-cost opticalwaveguides and filters are increasingly useful include internetapplications involving cloud computing, social networking,communications, entertainment, retail services, gaming, electronictrading, and advertising via wireless, wireline, and/or fiber opticalinterconnects such as Fiber To The Home (FTTH), Fiber To The Premise(FTTP), or more generally Fiber To The X (FTTX).

A limitation of conventional PICs is that they have a component packingdensity limited by the relatively long-range evanescent coupling oflight out of the single-mode waveguides, leading to a minimum “bendingradius” for the waveguides below which optical losses associated withthe bend are considered untenable. Waveguide size constraints inconventional PICs limits reduction of the physical dimensions of thePICs.

However, a new class of disordered photonic solids with large completeband gaps, namely, hyperuniform non-crystalline disordered solids, or“HUDS” was invented as claimed in WO2011/005530, which is herebyincorporated by reference. These new PBG materials, characterized bysuppressed density fluctuations (hyperuniformity), include disorderedstructures that are isotropic. This means that light propagates the sameway through the photonic solid independent of direction (which isimpossible for a photonic crystal). Experiments on a single 2d HUDS tileindicated that these structures exhibited complete isotropic photonicband gaps as detailed in WO2013/055503, which is also incorporated byreference.

FIG. 1A shows a HUDS structure 100 that includes walled cells organizedin an aperiodic lattice. A waveguide 115 is formed through HUDSstructure 100. FIG. 1B shows a zoomed-in view of structure 100 andwaveguide 115. FIG. 1B shows that walled cells (e.g. 121, 122, 123, 141,142, and 143) are organized in a non-periodic lattice structure 120 thatadheres to HUDS design requirements. Each walled cell includes wallssurrounding a void. The void may be filled with air, a vacuum, or amaterial other than air. For example, walled cell 122 includes walls122A enclosing a void 122B, which is designed to be filled with air inFIG. 1B. Although not specifically illustrated, walled cell 121 alsoincludes walled cells 121A and void 121B. Example walled cells 123, 141,142, 143 as well as the unlabeled walled cells that form lattice 120 inFIGS. 1A and 1B are similarly constructed.

Waveguide 115 was formed by creating a series of adjacent “defects” in apre-designed HUDS tile structure. In other words, waveguide 115 wasspecifically created by filling-in adjacent voids in adjacent walledcells. For example, if lattice 120 was made of silicon, adjacent cellswere filled with silicon so that waveguide 115 is a contiguous siliconwaveguide structure.

FIG. 2A illustrates an example of an optical structure 200 that includeswalled cells organized in a lattice 230, in accordance with anembodiment of the disclosure. A waveguide 215 is formed through opticalstructure 200. Optical structure 200 includes HUDS structure portions201A and 201B, adjusted interface portions 203A and 203B, and waveguide215. Adjusted interface portion 203A is disposed between HUDS structure201A and waveguide 215 and adjusted interface portion 203B is disposedbetween HUDS structure 201B and waveguide 215.

FIG. 2B shows a diagram of a zoomed-in portion 250 of FIG. 2A, inaccordance with an embodiment of the disclosure. FIG. 2B shows thatwalled cells (e.g. 212, 221, 222, 223, 241, 242, and 243) are organizedin a non-periodic lattice structure 230 that adheres to HUDS designrequirements. In one embodiment, waveguide 215 and lattice structure 230are formed of the same material (e.g. silicon) in a contiguousstructure. The walled cells that make up lattice 230 include wallssurrounding a void. The void may be filled with air, a vacuum, oranother material. For example walled cell 212 includes walls 212Aenclosing a void 212B, which is filled with air in FIG. 2B. Hence, voids(e.g. void 212B) in walled cells may be described as an air hole whenair fills a void in a walled cell. HUDS structure portions 201A and 201Binclude walled cells that are purely “HUDSian” in that they conform toHUDS design requirements. However, the walled cells in adjustedinterface portions 203A and 203B (e.g. 212, 221, 222, 223, 241, 242, and243) are adjusted relative to their design prior to definition of thewaveguide to facilitate a smooth boundary of waveguide 215 and do notnecessarily strictly adhere to HUDSian design principles. In oneembodiment, waveguide 215 shown as solid in FIGS. 2A and 2B is aphotonic crystalline or photonic quasicrystalline waveguide comprisingone or more rows of periodic or quasiperiodic elements. Adjustedinterfaces 203A and 203B transition in this embodiment from a periodicor quasiperiodic pattern on the smooth boundaries of waveguide 215 to ahyperuniform disordered pattern at an interface between the HUDstructure 201A and 201B and the adjusted interfaces 203A and 203B. It isunderstood that the brackets that indicate the position of adjustedinterfaces 203A and 203B and HUDS structures 201A and 201B are roughindicators of their position, as their positions may not necessarily bedefined by straight lines and instead may be defined walledcell-by-walled cell. In FIG. 2B, adjusted interface portions 203A and203B are one walled cell deep and only includes the walled cells thatcontact waveguide 215. However, in other embodiments, the adjustedinterface portion may be two or more walled cells deep. In other words,the transition between HUDS structure 201A and waveguide 215 may takeplace over two or more walled cells in order to further improve theperformance of waveguide 215, in terms of the efficiency with which ittransmits light, the spectral shape of its transmittance, the spectraldispersion of its transmittance, and/or other waveguide performancecharacteristics.

FIG. 4 shows that waveguide 215 was shown to be more efficient thanwaveguide 115, as data 416 (associated with waveguide 215) shows bettertransmission efficiency than data 417 (associated with waveguide 115),in chart 400. Chart 400 in FIG. 4 shows that the testing was completedfor optical signals in a near-infrared wavelength from 1500 nm to 1580nm, experimentally comparing the waveguide transmission spectra forwaveguides before and after the above-described design improvements atthe waveguide interface. Experiments were found consistent withnumerical simulation of the waveguide transmission spectra of structuressuch as 100 and 200, using Lumerical software. Lumerical's 2.5Deigenvalue eigenmode expansion (EME) solver MODE Solutions, Lumerical'sfully 3D “FDTD Solutions” software package, Lumerical's 3D FEM “DEVICE”software package, open source code such as MIT's MEEP, and othersoftware packages are applicable to simulating optical performance, forexample.

Referring back to FIG. 2B, the smooth boundaries of waveguide 215enclose walled interface cells 221-226 and 241-246. Walled interfacecells for the purposes of this disclosure are defined as the walledcells that contact the waveguide. Cell wall 232 is a wall of walledinterface cell 222 and encloses the void included in cell 222. Cell wall232 also defines and is integrated into a portion of the smooth boundaryof waveguide 215. The smooth boundary of waveguide 215 is smooth whencompared with the jagged waveguide boundary of waveguide 115. Forexample, in FIG. 1B, boundary 117A and 117B (also functioning as thewalls of walled cell 117) intersect at point 118. Boundary 117A is notparallel or close to parallel to boundary 117B. Rather boundary 117A isapproximately 30 degrees from parallel with boundary 117B. Additionally,cell 117 has two distinct walls that intersect at point 118. In FIG. 2B,walled interface cell 223 has smooth wall 233 that is a straight lineand functions as the boundary of waveguide 215 and as a wall of 233.Wall 233 does not come to a point. Walled interface cell 222 is adjacentto walled interface cell 223. Wall 232 of walled interface cell 222 isparallel with wall 233 of walled interface cell 223, in the illustratedembodiment. In FIGS. 2A and 2B, the smooth boundaries of waveguide 215are straight. However, curved and arbitrary waveguides can also befabricated that also have smooth boundaries, in accordance with theteachings of the present disclosure.

FIG. 2C shows a side view of example structure 299 that includes thefinite height perforated optical structure 200, in accordance with anembodiment of the disclosure. Structure 299 includes insulator layer 260disposed between handle substrate layer 255 and optical structure 200.FIG. 2C shows a cross section of the optical structure 200 illustratedin FIG. 2A as FIG. 2A shows a view of optical structure 200 through lineA-A′ in FIG. 2C. FIG. 2C shows that a cross section of waveguide 215 isdimensioned D1 281×D2 282 and is rectangular, in FIG. 2A-2C. In oneembodiment, dimension D1 281 is 500 nm and dimension D2 is 200 nm. D2may be 204 nm or 220 nm in some embodiments. In some embodiments,portions of insulator layer 260 are removed beneath waveguide 215 tofacilitate the desired light propagation in waveguide 215. In oneembodiment, insulator layer 260 includes silicon-dioxide.

Structure 299 is one fabrication structure that may be utilized tofabricate optical structure 200 using CMOS fabrication techniques andavailable silicon-on-insulator (“SOI”) materials. In one embodimentoptical structure 200 is formed from a solid semiconductor layer (e.g.silicon) using a subtractive process. This allows HUDS structures to beused as cladding for silicon waveguides. In one embodiment, a SOI waferwith 220 nm crystalline silicon height and a 2 um buried oxide layer isused to fabricate HUDS waveguides using standard electron beamlithography and inductively-coupled plasma reactive ion etching.Photolithography can also be used to fabricate HUDS waveguides.

Starting with a solid silicon layer, the voids in each walled cell canbe subtracted (via etching process, for example) from the solid siliconlayer, which leaves lattice 230 and waveguide 215 as a contiguoussilicon structure. In one embodiment, the voids are left as air holes.In one embodiment, the voids are a vacuum. In one embodiment, the voidswith the walled cells are filled with a material different from thematerial that forms lattice 230 and waveguide 215. In one embodiment,the voids are filled with a fill material having a first index ofrefraction that is different than an index of refraction of the materialthat forms the lattice 230 and waveguide 215. The fill material and thematerial forming lattice 230 may have oppositely-signed dependence oftheir indices of refraction on temperature. In other words, whentemperature increases, the index of refraction of one material increaseswhile the other index of refraction of the other material decreases. Inone embodiment, the fill material includes titanium-dioxide and thelattice material is silicon. The index of refraction of titanium-dioxidedecreases when temperature increases while the index of refraction ofsilicon increases when the temperature increases, thus titanium-dioxideand silicon have oppositely-signed dependence of their indices ofrefraction on temperature. This use of a fill material having anopposite and offsetting thermo-optic coefficient makes the opticalperformance characteristics of structures such as 200 more temperaturestable. In one embodiment, the first index of refraction of the fillmaterial is greater than air and less than the second index ofrefraction of the material that forms the walled cells in lattice 230.Silicon-dioxide may also be used as a fill material. Titanium-dioxideand silicon-dioxide can be disposed in the voids using known processesas these materials are commonplace in CMOS fabrication. In oneembodiment, a nitride is used to fill voids. In other embodiments, layer200 is another group V material such as germanium, or a combination ofsilicon and germanium, or another material. In other embodiments, layer200 is a III-V material such as GaAs, GaInAs, or another III-Vengineered material. In other embodiments layer 200 might be a polymer,a perovskite, another electrooptic material, or any number of othermaterials having an appropriate bulk dielectric constant and bulkoptical transmittance. Other embodiments designed for operation atelectromagnetic wavelengths outside the optical spectrum will use othermaterials having appropriate bulk real and imaginary dielectricconstants appropriate to the wavelength of design. At microwavefrequencies, for example, alumina is an example of a material havingappropriate real and imaginary dielectric constants to be used as thewalls of the structure. In other embodiments, the walls can be made outof commercial plastic materials that are used in 3d-printers.

In one embodiment, the walls are made of silicon, and the latticeconstant of optical structure 200 is 499 nm, corresponding to atransverse-electric (“TE”) polarization PBG with zero density-of-statecentered around 1550 nm. The wall thickness of the walled cells inlattice 230 may be between 80 nm and 150 nm.

FIG. 3A illustrates boundaries for HUDS tile designs that can be used togenerate optical structure 200, in accordance with an embodiment of thedisclosure. The design of a HUDS tile (including tile section 310 andtile section 320) have a boundary condition along edge c which isoptimized for a situation in which edge c is an edge of a straightwaveguide such as waveguide 215. Edge a of the tile has a boundarycondition set to match to an adjoining HUDS tile having a boundarycondition a′. Edges d and d′ have boundary conditions optimized so as toboth enable straightforward interconnection of d and d′ and to smoothlytransition between the different boundary conditions along edge c andedge a.

One or more of several methods can be used in the optimization of theHUDS pattern. For example, one can optimize the HUDS pattern usingwaveguide transmission as the metric to determine the optimal pattern.In other situations, flatness of transmission across a particularwavelength range may be the preferable metric. In yet another situation,the preferable metric may be the quality factor or Q of apurposely-designed resonant cavity being used for example as a filter.In yet another situation, the preferable metric may be the modulationdepth of a modulator. For a highly complex PIC such as a transceivercomprising waveguides, wavelength filters, modulators, and othercomponents, the relevant metrics may be the bit rate and bit error rate(BER) of the transceiver. In some cases it can advantageously savesignificant numbers of computational cycles to initially compute,monitor, and minimize the on-axis power in the Fourier transform of thestructure (which will approach zero as the structure becomesincreasingly hyperuniform) prior to optimizing the HUDS structure withrespect to the overall optical performance metrics of the photonicintegrated circuit as a whole.

The boundary conditions for a HUDS structure is defined by tile section310 and 320. Along the straight edge of waveguide 215 (edge c) aperiodic (e.g. photonic crystalline) or quasi-periodic (e.g. photonicquasi-crystalline) pattern is applied in the adjusted interface portions203A and 203B. As crystalline and quasi-crystalline patterns are bothhyperuniform, they can both be blended into a hyperuniform disorderedpattern in the purely HUDSian remainder of tile sections 310 or 320. Thearea shaded by the diagonal hatch lines is adjusted interface portions203A and 203B in which the periodic or quasi-periodic pattern on edge cis transitioned from periodic or quasiperiodic to hyperuniformdisordered. Boundary conditions along edges labelled d and d′ aredesigned to facilitate both the transition from periodic orquasiperiodic to HUDS, and the smooth connection of edge d to edge d′.

FIG. 3B illustrates a more complex boundary condition that might beused, for example, to create a particularly compact edge coupler, inaccordance with an embodiment of the disclosure. The boundary conditionin this case is designed to facilitate use of a bi-quadratically-flarededge coupler, narrowing-down to mate with a straight waveguide 315.Boundaries c and c_(r) can in this case be mirrors of one another.Boundaries q and its mirror q_(r) forms a quadratic or bi-quadratictaper, although FIG. 3B may not be an exact representation of aquadradic or bi-quadratic taper. Boundaries a and a′ are designed tointerconnect with one another. Boundary d is designed to interconnectwith boundary d′. Boundary d_(r) is designed to interconnect withd_(r)′. Tile section 330 is a HUDS structure, except for adjustedinterface portion 303A, which is similar to adjusted interface portion203A. Tile section 340 is a HUDS structure, except for adjustedinterface portion 303B, which is similar to adjusted interface portion203B. Both tapers and inverse tapers are possible depending on the shapeof the taper, the relative dielectric constants of the walls and holes,and the design of the surrounding HUDS. The taper can also be engineeredinto the perforations around the waveguide.

FIG. 3C shows a HUDS tile having tile sections 350 and 360, inaccordance with an embodiment of the disclosure. The HUDS tile shown inFIG. 3C shows that arbitrarily-curved waveguide shapes such as waveguide415 can be fabricated as well as straight waveguides 215. Tile section350 is a HUDS structure, except for adjusted interface portion 403A,which is similar to adjusted interface portion 203A. Tile section 360 isa HUDS structure, except for adjusted interface portion 403B, which issimilar to adjusted interface portion 203B.

In one example, to design the example HUDS tiles illustrated in FIGS.3A-3C, the boundary of each of the tile sections are defined and a HUDSstructure is generated for those boundaries by employing a centroidaltessellation of a hyperuniform point pattern to generate a “relaxed”dual lattice, whose vertices were necessarily trihedrally coordinated byconstruction. More details about the particular design is detailed in“Designer disordered materials with large complete photonic band gaps,”M. Florescu, S. Torquato, and P. Steinhardt, Proc. Natl. Acad. Sci. USA106, 20658 (2009), which is hereby incorporated by reference.Additionally, the descriptions disclosed in WO2011/005530 andWO2013/055503 may be used in designing the HUDS structures within theboundaries, both documents which are hereby incorporated by reference.

After a HUDS pattern or structure is generated using the boundaryconditions of each tile section, the boundary nearest the edge of thewaveguide is adjusted to generate the adjusted interface portions. It isappreciated that in FIG. 3A for example, the edge c is also theedge/boundary of waveguide 215, and thus, one of the edges of thewaveguide is also a boundary condition of the HUDS structure that isgenerated initially. The adjusted interface portions can be generated bymanually adjusting the initial HUDS structure at the edge of thewaveguide at the design phase and then the designs can be simulated todiscern the optical efficiency of the waveguide.

Alternatively the adjusted interface portions can be incrementallymodified in a software program and then simulated to narrow in on ahighly efficient structure for the adjusted interface portions.

FIG. 5A illustrates an optical structure 500, in accordance with anembodiment of the disclosure. Optical structure 500 includes HUDSstructures 501A and 501B formed by walled cells organized in anon-periodic lattice 530. Optical structure 500 also includes awaveguide 515 and a resonant cavity 533 formed by eliminating severalwalls in close proximity to a boundary of waveguide 515. In FIG. 5A,optical structure 500 also includes adjusted interface portions 503A and503B. Further adjustments in the immediate vicinity of the resonantcavities can be formed in HUDS structures without necessarily havingadjusted interface portions. In FIG. 5A, adjusted interface portion 503Ais disposed between HUDS structure 501A and waveguide 515 and can beextended in the vicinity of resonant cavity 533 to surround resonantcavity with one or more rows of cells encircling the cavity.

FIG. 5B shows a zoomed-in version of optical structure 500, inaccordance with an embodiment of the disclosure. In FIG. 5B, adjustedinterface portion 503A includes at least one row of walled interfacecells (e.g. 521-525) disposed between waveguide 515 and HUDS structure501A. Boundaries of waveguide 515 enclose walled interface cells that(e.g. 521-525) that are disposed at the boundary of the waveguide. Inthe illustrated embodiment, resonant cavity 533 is disposed between HUDSstructure 501A and adjusted interface 503A. Waveguide 515 is dimensionedto transmit an optical signal having frequencies in a given bandwidth(e.g. 1500 nm to 1600 nm, 1300 nm to 1350 nm, or another wavelength bandimportant to communications or ranging, including visible wavelengths inthe event that the structure is made from a material with appropriatebulk transparency in the visible, THz wavelengths, microwavewavelengths, etc.) and resonant cavity 533 is configured to be resonantat a frequency band (e.g. a frequency band centered around 1552 nm)within the frequency of the bandwidth of the waveguide 515. In otherwords, resonant cavity 533 is configured to filter out a portion of theoptical signal guided by waveguide 515. Resonant cavity 533 is made byforming a “defect” in the HUDS structure 501A by removing walls fromsome of the walled cells in lattice 530. In the illustrated embodiment,the walls of six walled cells were removed to form resonant cavity 533.In the illustrated embodiment, resonant cavity 533 is defined by anenlarged hole in lattice 530. The enlarged hole is larger than a holesize of any one of the walled cells in a defect-free portion of thelattice where walls of the walled cells of the original lattice have notbeen removed. In this case, the resulting mode is an “air mode” since ittraps light primarily in the air hole rather than in the silicon walls.

FIG. 5C illustrates an optical structure 550 having a resonant cavity583, in accordance with an embodiment of the disclosure. Opticalstructure 550 is similar to optical structure 500 shown in FIG. 5B,except that the resonant cavity in optical structure 550 is made by oneof the walled cells in the lattice 580 being filled. Resonant cavitiesmay also be formed by filling or partially filling at least one void ofwalled cells in lattice 580. In FIG. 5C, resonant cavity 583 is formedby filling (completely) a void of a walled cell with silicon, wherelattice 580 is also made of silicon. It is appreciated that infabrication the phrase “filling a void” may translate to refraining fromcreating the void in the first place, for example, when silicon is beingetched to generate lattice 580 and waveguide 565. In FIG. 5C, resonantcavity 583 is two walled cells from waveguide 565. Other resonantcavities (resonant defects) besides those discussed in this disclosurecan be used, including examples of HUDSian defects described inPCT/US2012/055791 (WO2013055503A1) and “Optical cavities and waveguidein hyperuniform disordered photonic solids” by Florescu, Steinhardt, andTorquato, Phys Rev B, 2013, both documents which are herein incorporatedby reference.

Similarly to optical structure 200, waveguide 515/565 and latticestructure 530/580 may be formed of the same material (e.g. silicon) in acontiguous structure. Each of the walled cells that make up lattice530/580 include walls surrounding a void. The void may be filled withair, a vacuum, or another material. And, voids in walled cells may bedescribed as an air hole when air fills a void in a walled cell. Alsosimilarly to optical structure 200, in one embodiment, the voids in thewalled cells in optical structure 500/550 are filled with a fillmaterial having a first index of refraction that is different than anindex of refraction of the material that forms the lattice 530/580 andwaveguide 515/565. The fill material and the material forming lattice530/580 may have oppositely-signed dependence of index of refraction ontemperature. In one embodiment, the fill material includestitanium-dioxide and the lattice material is silicon. An oxide or anitride is used to fill the voids in some embodiments. The walls can bemade of other semiconductors as described previously such as III-Vmaterials and their alloys, or other Group IV materials such as Ge orSi/Ge alloys, or electrooptic materials such as LiNbO, BaTiO3, orelectro-optic polymers, specially-doped plastics having engineered bulkreal and imaginary dielectric constants, commercial or more recentlydeveloped plastics such as are available for use with macroscopic andnanoscopic 3d printers, and ceramic materials such as alumina.

HUDS structure portions 501A/551A and 501B/551B include walled cellsthat are purely “HUDSian” in that they are designed and adhere to HUDSrequirements and principles. However, the walled cells in adjustedinterface portions 503A/553A and 503B/553B are adjusted to facilitate asmooth boundary of waveguide 515/565 and do not necessarily strictlyadhere to HUDSian design principles. In one embodiment, adjustedinterfaces 503A/553A and 503B/553B transitions from a periodic orquasiperiodic pattern on the smooth boundaries of waveguide 515/565 to ahyperuniform disordered pattern at an interface between the HUDstructure 501A/551A and 501B/551B and the adjusted interfaces 503A/553Aand 503B/553B.

Designing optical structure 500 and 550 is similar to the design ofoptical structure 200, except that after the HUDS structure is designedand adjusted to form the adjusted interface portion, optical cavity533/583 is formed. Adjusted interface portions 503A/553A and 503B/553Bcan be generated using the same techniques described in association withadjusted interface portions 203A and 203B. Once the design of opticalstructure 500 or 550 is determined, that design can be fabricated (e.g.etched in silicon).

FIG. 6 illustrates a chart showing the simulated performance of awaveguide in example optical structure 500 using a 2.5d eigenvaluesolver. FIG. 6 shows that infrared light between 1500 nm and 1600 nmpropagates through waveguide 515 at very high efficiency, although avery narrow frequency band (1544 nm-1547 nm) is trapped (resonates) inresonant cavity 533. Hence, resonant cavity 533/583 and waveguides515/565 are configured to block (a.k.a. “drop”) the specified frequencyband and pass the remaining bandwidth of the optical signal throughwaveguides 515 and 565, respectively. Therefore, FIG. 6 indicates thathigh performance filtering is achievable using the resonant cavitiesdescribed in FIGS. 5A-5C. Furthermore, the resonant cavities describedin FIGS. 5A-5C have also been shown to possess improved temperaturestabilization properties when compared to conventional solutions such asmicro-rings. FIG. 7A illustrates the transmission of waveguide 515 whenresonant cavity 533 is tuned to filter out a frequency band centeredaround 1543.1 nm. As FIG. 7A illustrates, there is very littlewavelength shift in the filter performance even with a 40° C. shift intemperature. One numerical simulation showed that the temperature shiftwould be ˜0.15 pm/K°. FIG. 7B shows the wavelength shifts inconventional optical filters can be three or more nanometers over thesame 40° C. range. Conventional micro-ring resonators, in comparison,have a wavelength shift of ˜60-90 pm/K.

FIGS. 8A and 8B illustrate a HUDS-based electrically-controlled opticalmodulator 899 that can be included in a PIC, in accordance with anembodiment of the disclosure. Side view FIG. 8A shows an insulator layer810 disposed on a handle substrate 805. Insulator layer 810 may besilicon-dioxide and the handle substrate may be silicon. HUDS structures801A and 801B are formed by walled cells organized in a lattice and aredisposed on the insulator layer. HUDS structures 801A and 801B can havethe same properties as HUDS structures 201A/501A and 201B/501B withregard to the walls and voids. In FIG. 8A, adjusted interface portion803A is disposed between HUDS structure 801A and resonant structure 833and adjusted interface portion 803B is disposed between HUDS structure801B and resonant structure 833. Adjusted interface portions 803A and803B are similar to adjusted interface portions 203A and 203B, exceptthat the lattice is adjusted to the boundary of resonant structure 833as well as being adjusted to the boundary of waveguide 815, in theillustrated embodiment.

A first doping region is disposed within HUDS structure 801A. In theillustrated embodiment, the first doping region includes dopingsub-regions 821 and 822. Doping sub-region 821 is N+ doped and dopingsub-region 822 is N doped. Doping sub-region 821 is N+ doped tofacilitate electrical conduction with first electrical contact 831.Doping sub-region 822 is disposed between resonant structure 833 anddoping sub-region 822. In other embodiments (not illustrated), the firstdoping region is not separated out into sub-regions, but has ahomogenous doping concentration between resonant structure 833 and firstelectrical contact 831. A second doping region is disposed within HUDSstructure 801B and has an opposite doping polarity as the first dopingregion. In the illustrated embodiment, the second doping region includesdoping sub-regions 823 and 824. Doping sub-region 823 is P doped anddoping sub-region 824 is P+ doped. Doping sub-region 824 is P+ doped tofacilitate electrical conduction with second electrical contact 832.Doping sub-region 823 is disposed between resonant structure 833 anddoping sub-region 824. In other embodiments (not illustrated), thesecond doping region is not separated out into sub-regions, but has ahomogenous doping concentration between resonant structure 833 andsecond electrical contact 832.

In FIG. 8A, waveguide 815 is disposed between the resonant structure 833and is configured to guide an optical signal. In FIG. 8A, an air spacevoid is situated between sections of insulator layer 810 and is disposedbetween optical structure 800 and handle substrate 805. Removing aportion of insulator layer 810 to make room for air provides symmetricalair cladding on both the top and bottom surfaces of the device. It isappreciated that handle substrate 805 may be used to facilitate CMOSfabrication techniques and that it may ultimately be thinned or removed,and that asymmetric cladding designs without removal of the underlyingoxide may be preferred for some applications or for potentially improvedmanufacturing yields.

FIG. 8B shows a semi-transparent plan view of optical modulator 899, inaccordance with an embodiment of the disclosure. The example plan viewshows that resonant structure 833 includes two semi-circle shapes, oneon either side of waveguide 815. FIG. 8C shows one example of aconceptual illustration of a resonant structure 833A that can be used asa resonant structure 833.

FIG. 8D shows an example resonant structure 833B that can be used asresonant structure 833, in accordance with an embodiment of thedisclosure. FIG. 8D shows resonant structure 833B being a perforatedstructure that connects the lattice 880 and waveguide 865. In FIG. 8D,waveguide 865 is a photonic crystal waveguide having three rows ofcircular perforations on both sides of an unperforated central strip866. Third row 843 of the circular perforations is farthest from centralstrip 866 while first row 841 is closest to central strip 866. Secondrow 842 of the circular perforations is disposed between third row 843and the first row 841 of the circular perforations. In one embodiment,all the circular perforations are the same size.

In the illustrated embodiment, perforated resonant structure 833Bincludes an outer segment of eight circular perforations 873. Eachcircular perforation 873 is offset from its respective row by a firstoffset distance. The first offset distance is away from central strip866, as indicated by the white arrows. In one embodiment, the firstoffset distance is 3 nm. Perforated resonant structure 833B alsoincludes a middle segment of five circular perforations 876. Eachcircular perforation 876 is offset from its respective row by a secondoffset distance that is greater than the first offset distance. Thesecond offset distance is away from central strip 866, as indicated bythe white arrows. In one embodiment, the second offset distance is 6 nm.Perforated resonant structure 833B also includes a middle segment of twocircular perforations 879. Each circular perforation 879 is offset fromits respective row by a third offset distance that is greater than thesecond offset distance. The third offset distance is away from centralstrip 866, as indicated by the white arrows. In one embodiment, thethird offset distance is 9 nm. The middle segment of circularperforations 876 is disposed between circular perforations 873 of theouter segment and the circular perforations 879 of the inner segment.

The circular perforation holes can be etched from silicon to fabricateresonant structure 833B. Having waveguide 865, lattice 880, andperforated structures 833B all be a continuous structure lends itself toa simplified CMOS fabrication as all of the features can simply beetched from silicon. Perforated resonant structure 833B is configured tobe resonant at a frequency band that is a subset of a bandwidth ofoptical signal 896 and modulated optical signal 897 includes thatfrequency band while the remaining bandwidth of optical signal 896 isnot transmitted in modulated optical signal 897.

In one embodiment, the lattice spacing and fill ratio of the walledcells in the lattice of HUDS structures 801A/B is 473 nm and 37%,respectively. The lattice spacing and fill ratio when adjusted interfaceportions 803A/B transition from the photonic crystal to the HUDS may be420 nm and 55%, respectively.

In operation, an optical signal 896 propagating through waveguide 815can be modulated into modulated optical signal 897 by changing anelectrical modulation signal coupled to electrical contacts 831 and 832.Modulating the voltage across electrical contacts 831 and 832 changes acorresponding electrical field across resonant structure 833. At zerovolts on electrical contacts 831 and 832, waveguide 815 and perforatedresonant structure 833B are configured to function as a narrow pass bandfilter that transmits light (as an optical signal) only at the resonantfrequency of the cavity. When a voltage (e.g. 2 VDC) is applied toelectrical contacts 831 and 832, the index of refraction of resonantstructure 833 changes, spoiling the cavity Q, and thus shifting thewavelength of the light of the optical signal. Therefore, the opticalsignal can be modulated in response to an electrical modulation byshifting the wavelength of the light propagating through waveguide 815.A controller (not illustrated) including logic, a microprocessor, and/ora Field-Programmable-Gate-Array may be coupled to the electricalcontacts to drive the electrical modulation signal. The controller maybe coupled to a plurality of electrical contacts to modulate the opticalsignals in a plurality of waveguides by adjusting the index ofrefraction of a resonant structure. It is appreciated that sincedifferent voltages applied to electrical contacts 831 and 832 generatedifferent index of refraction changes in resonant structure 833,different voltages correspond to different wavelength shifts. Thus,using different analog voltages in an electrical modulation signal canresult in multiple different (distinct) wavelength outputs of theoptical signal allowing grey-scale control of the outputted opticalsignal.

Although waveguide 815 is illustrated being between resonant structure833 in FIGS. 8A and 8B, electrical contacts (and associate dopingregions) can also be used in conjunction with other resonant structuresto modulate optical signals propagating through a waveguide. Forexample, resonant cavity 533 or 583 could also be used as a resonantstructure. FIG. 8E shows a plan view of resonant cavity 533 having firstand second doping regions disposed in the semiconductor lattice tochange the electrical field (and thus index of refraction) of resonantcavity 533 to modulate an optical signal propagating through waveguide515, in accordance with an embodiment of the disclosure. Electricalcontacts 831 and 832 are conductively coupled to the doping regions toprovide the modulation signal. In this embodiment, resonant cavity 533and waveguide 515 are configured to block the frequency band thatresonant cavity 533 is tuned to and pass the remaining bandwidth of theoptical signal propagating through waveguide 515. In the embodimentillustrated in FIG. 8E, waveguide 515 does not divide the resonantstructure, as in FIG. 8A-8D. In other words, the resonant cavity in FIG.8E is “adjacently coupled, whereas the resonant cavity in FIG. 8D is“in-line coupled.”

FIG. 8F shows a plan view of resonant cavity 583 having first and seconddoping regions disposed in the semiconductor lattice to change theelectrical field (and thus index of refraction) of resonant cavity 583to modulate an optical signal propagating through waveguide 565, inaccordance with an embodiment of the disclosure. Electrical contacts 831and 832 are conductively coupled to the doping regions to provide themodulation signal. In this embodiment, resonant cavity 583 and waveguide565 are configured to block the frequency band that resonant 583 cavityis tuned to and pass the remaining bandwidth of the optical signalpropagating through waveguide 565.

FIG. 9 illustrates a block diagram of an example optical transceiver 999that includes a HUDS PIC 980, in accordance with an embodiment of thedisclosure. Optical transceiver 999 is coupled between optical switchrouter 911 and optical switch router 912. An electrical input port 931of optical transceiver 999 is coupled to receive an incoming opticalsignal from optical switch router 911 via optical fiber 921. An outputport 932 of optical transceiver 999 is coupled to transmit an outgoingoptical signal from optical transceiver 999 to optical switch router 912via optical fiber 922. PIC 980 includes optical structure 500, opticalreceiver 960, controller 910, optical modulator 899, optical structure200, and light source 925. FIG. 9 shows one example of how the disclosedoptical structures can be used within a network, although many moreexamples (unillustrated) are possible. The compactness of the resonantstructures compared to alternatives such as conventional microringresonators means advantageously allows for substantially densermultiplexing of multiple wavelengths on a single chip, as might berequired, for example, to fabricate a 100 Gb/s or 1 Tb/s modulator on achip by integrating together on a single chip the PIC elements requiredto control 10s or 100s of wavelengths each operating at 10 Gb/s.

In FIG. 9, optical structure 500 receives the incoming optical signalvia input port 931. Optical structure 500 filters the incoming opticalsignal according to the tuning of resonant cavity 533. Hence, only asmall frequency band of the optical signal will ultimately propagatethrough waveguide 515 and be received by optical detector 960. It isappreciated that many optical structures 500 that are tuned to differentfrequency bands can be coupled to input port 931 to function as anoptical splitter, each filter sending a different frequency band to adifferent optical detector. The resonant structures can be configuredwith their coupling waveguides to either pass or drop signals ofparticular wavelengths. A plurality of optical structures 500 (tuned todifferent frequency bands) can also be cascaded together to achievedifferent filtering characteristics. Alternatively, multiple wavelengthsincoming from switch 911 can be edge-coupled to optical structure 500,split-up on chip in a parallel fashion, fed separately to an array ofphotoreceivers 960, after which the controller 910 can drive an array ofoptical modulators 899 each tuned to a different wavelength, thenmultiplexed together in 200 into a single waveguide, out-coupled to afiber with a broadband edge coupler coupled to output port 932.

Controller 910 generates modulation signal 923 in response to receivingthe filtered optical signal from optical structure 500 via opticaldetector 960, which may be a photodiode. Modulation signal 923 is drivenby controller 910 to modulate a voltage across the electrical contacts831 and 832 of optical modulator 899. Optical modulator 899 is coupledto receive transmission light from light source 925 (e.g. laser or LED)in waveguide 815 and modulate the transmission light by changing theelectric field around resonant structure 533/583. The modulatedtransmission light may then be guided by waveguide 215 in opticalstructure 200 to output port 932 and be transmitted to switch 912 viaoptical fiber 922. Of course the illustrated embodiment of FIG. 9 isexemplary and is only one example of how the disclosed opticalstructures can guide, filter, and modulate light for network purposes.

The utility of the temperature-stabilized PBG and HUDS-based resonantoptical cavities and associated photonic integrated circuits making upthe optical interconnects through which data is transmitted inHUDS-enabled networking and/or sensing systems can be better-understoodaccording to the value which HUDS-enabled interconnects formed by theinventive HUDS components provide to the network as a whole. WhileMetcalf's Law asserts that the value of a network scales as the squareof the number of nodes that are interconnected, Odlyzko has argued thatthe value is actually n log(n). Both these estimations overlook the factthat the value of the network also depends sensitively on the rate ofcommunications between the nodes. One way to include inter-node bitrates in the analysis of the value of a network of n nodes is toconsider a frozen instant in time during which the number n of nodescommunicating will depend sensitively on the data rate at which nodesare able to communicate. As an extreme example, consider a network inwhich nodes communicate synchronously, only once per second. Assessingthe value of such a network at the half-second mark would result in avaluation of zero, as there would be no communication whatsoever betweenthe network elements at this moment of time. Legacy networksinterconnected for example at 1 Gb/s, would have had vanishingly smallinstantaneous value for time slices as short as femtoseconds, as thenumber of nodes n communicating during these very closely-space timeslices would be vanishingly small. It is therefore clear that the numberof nodes n in a network varies as a function of time and that therelevant quantity in assessing the value of the network as a whole isnot simply the number of nodes in the network, but the product of thenumber of nodes with the interconnection bit rate R attributed to thosenodes. Adapting Metcalf's Law to incorporate the added-value of theinterconnect bit rate leads to the value of the network scaling notsimply as n² but as (nR)².

To the above description of the value to a network of an increase in theinterconnect bit rate, it is important to add an understanding of hownetworks create revenue, and how the bit rates, energy efficiency,initial capital cost and other relevant interconnect specificationscontribute to the revenue-generating capability of the network. Thenumber of business models for using the internet to generate revenue hasflourished. Several exemplary optical networking systems on which thesekinds of businesses operate will be examined by way of example,particularly in light of the impact of the reduced energy requirementsand potentially improved temperature stability of the comprisingcomponents impacts the utility of the business.

First, consider the down-loading of movies from companies such asNetflix. To the extent that the movies can be downloaded faster than theuser can watch them may mean that the value to a consumer of a moviebeing purchased may scale less than linearly with the speed of anend-user's interconnect. That is, just because the end-user can downloadtwo movies in 10 minutes rather than just one movie in 10 minutesdoesn't necessarily mean that the end user will either download twomovies rather than one, or that he is willing to pay twice as much for asingle movie as he would pay were his internet connection half as fast.While a faster interconnect rate certainly improves the end-user'sconsumer experience, the value which he attributes to the bit rate ofhis interconnection may scale sub-linearly with the bit rate of hisinterconnection. Depending on whether the user's electrical power isprovided by a wall plug as is common today rather than a battery orsolar panel as may be more common in the future, the user may not beparticularly sensitive to the energy requirements of the download. Thesituation at the nearest content delivery network center, by contrast,is substantially more sensitive to the performance features and energybudget of the interconnect and its temperature stabilization circuitry,in that the content deliver network needs to build and powersufficiently high bit rate capacity to multiplex as many video downloadsas their customers may demand during anticipated peak hours ofoperation.

A second example would be in the case of a networking system designed tosupport teleconferencing. In this case, the video signals need to bestreamed in real-time rather than asynchronously downloaded. Networkcongestion anywhere in the network can in this case result in completebreakdown of the teleconference experience. In this case, networkinterconnections capable of providing twice the bit rate at less thantwice the power are substantially more likely to be able to supporttwice the traffic, particularly at peak loads. In this case, the utilityto the teleconference service provider of the interconnects' bit ratemay, in a practical sense, scale with the amount of revenue-generatingtraffic which it can support. Energy savings associated with reducedtemperature control requirements can be particularly enabling inscenarios where energy is expensive and/or unreliable or intermittent.

Third, consider the utility of increased bit rate to a network systemdesigned to implement electronic trading. In this case, while energy perbit costs may pale in comparison to the value of a single trade, havinga faster interconnection rate is known to lead directly to the captureof trading revenues. Reduced temperature stabilization circuitry can inthis case lead to denser interconnects, more closely-spaced servers, andreduced latency. To the extent that the fastest interconnect wins, theentire value of a company's trades may indeed be directly attributed tofactors such as data rate and latency.

A fourth case for consideration may be the utility of the subjectinvention in network systems designed to generate revenue viaadvertising on the internet. Such revenue-generating systems areparticularly relevant to search engines and social networks operatingout of increasingly energy-hungry data centers. To-date, thesenetworking systems and the businesses which they've enabled have reliedon the fact that computer processors are cheap, interconnects arecheaper, and interconnect energy costs are negligible. As traffic grows,datacenters have expanded by adding additional processors.Interconnection capital costs between the processors, initially smallrelative to the costs of the processors, are now becoming morecomparable to the costs of the processors. As well, the energy costsassociated with interconnects, initially small relative to the amount ofenergy required to run the processors, are now becoming significant.What this means is that energy constraints on data centers contributetoward limiting how high an interconnect data rates is deployable in apractical sense. Increasingly, energy costs therefore conspire togetherwith capital costs to determine the useful computational output (a.k.a.“good put”) of a data center. Packet-routing systems such as those usedin data centers were brilliantly-designed to respond robustly tocongestion; packets dropped in the presence of congestion are re-sent.But while the resending of dropped packets beneficially assures that thedata eventually arrives at the destination for which it was intended,the need to re-send the packets inarguably reduces the “goodput” of theequipment sending the data, the equipment receiving the data, and thedata center as a whole. In datacenter business models, the value ofimproved interconnect bit rate can be related directly to the goodput ofthe datacenter in terms of the return-on investment (ROI) which theadvertising business model and/or social networking business model makeson the core data center operation which executes the company'scomputational methods.

As a fifth example, consider networking systems designed to supportretail sales. Large online retailers find that users searching for itemshave limited patience in waiting for a search algorithm to complete. Forthis reason, these retailers have been motivated to size their datacenter operations for their busiest season. Search algorithms involvelots of communication within and between datacenters. The utility of thenetworking systems designed to support retail sales depends in apractical sense quite sensitively on the profits earned by onlineretailers, after payment of both the capital (including interconnect,computing, and cooling hardware, costs of which depend on theperformance specifications of the interconnect) and operational costs ofthe data centers (which includes an increasingly large component due tothe energy requirements of the data interconnects). Financial profitsand associated viability of online retail businesses are hence directlylinked to performance characteristics of the interconnects over whichtheir servers communicate, such as data rate, energy efficiencyincluding energy required to achieve necessary temperaturestabilization, and bandwidth density per unit chip area.

As a sixth example, consider networking systems designed to broadlysupport cloud computing systems. Such systems increasingly deploydynamically-programmable network resources designed to flexibly adapttheir computing and communications resources so as to dynamically-adaptthe efficiency or “goodput” of their systems depending on which one ormore of the above-described systems might be in demand by theircustomers. Dynamic reconfiguration of network resources fordynamically-controllable cloud computing network systems requiresincreasingly dense integration of network transceivers withsoftware-controlled electronics control and monitoring systems. Reducingthe temperature stabilization required of interconnects enables theinterconnects to be arranged in a substantially more compact manner. Thecompactness, energy efficiency, high bandwidth, and prospects forhigh-density chip-scale implementation of complex control and monitoringfunctions on the inventive HUDS PICs enable substantiallyhigher-performance cloud computing networking systems than wouldotherwise be possible.

The six optical networking systems enabled by the inventivelytemperature-stabilized PBG resonant optical cavities, and describedabove, are not meant to be limiting, but were chosen to illustrate thesubstantial utility of increased interconnect bit rates and how thevalue of interconnect bit rates scales vertically through key networkingsystems, the currently high utility of which will be substantiallyincreased by inventively designing these networks to comprise theinventively temperature-stabilized resonant optical cavities. Theutility of interconnects in networking applications is substantiallygreater than just the transmittal of data from one point to another.

Interconnects are a key enabling component in networks. Particularly asoptical interconnects move closer and closer to the computer processors,and indeed into the computer processor chips themselves, the utility ofinterconnects increasingly depends on the extent to which they can bemanufactured via the same massively-parallel manufacturing techniqueswhich have been used to advantage in making the costs of computerprocessors drop as a function of time in accordance with Moore's Law.One way to do this is to develop new approaches for the design of highperformance photonic integrated circuits having the largest possiblebandwidth density and/or component density per unit chip area while atthe same time enabling the design and fabrication of increasinglycomplex, energy-efficient, high bit-rate photonic integrated circuits.

One method or approach for implementing adjustments alongarbitrarily-curved boundaries as are likely to surround a complexphotonic integrated circuit is described in “Arbitrary waveguides innear-hyperuniform photonic slabs: Towards a general purpose modulardesign platform for integrated photonic circuits,” by Amoah andFlorescu. This paper describes a novel bottom-up design strategy forplanar non-straight optical waveguides. Unlike traditional methods wherea template is generated first and waveguides are designed accordingly,the waveguide is defined first and an optimized structure is then builtaround it. Notably, traditional triangular photonic crystal (PhC)designs can naturally be accommodated by this strategy, which is apromising candidate towards a unified design platform for complexoptical microcircuits, applicable to CMOS technology. Using finitedifference time domain (FDTD) computer simulations the transmissionproperties of bend waveguides in planar photonic slabs was evaluated andsignificant transmission can be achieved in the low-loss spectral range.Transmission losses as low as 13% of the maximal straight waveguidetransmission were observed in the vicinity of 1.6 micron wavelength forTE radiation in a 220 nm thick suspended membrane with refractive indexn=3.475 corresponding to silicon.

The field of photonics has progressed remarkably through the developmentof subwavelength nano-structuring technologies. This is now leading toincreasing on chip integration of photonic devices. Devices such asultralow-threshold electrically pumped quantum-dot PhC nano-cavitylasers such as described in “Ultralow-threshold electrically pumpedquantum-dot photonic-crystal nanocavity laser,” by Ellis et al., 2011;and fast low power electro-optic PhC nano-cavity modulators demonstratea high level of synergy between photonics and electronics. Whileintegrated optical circuits are being intensively researched, designfreedom remains limited. Current designs are either very simplistic(strip waveguides or PhCs based on simple periodic templates, or arecounter-intuitive to the human designer and computationally expensive togenerate. It was recently demonstrated that large band gaps are not onlyachievable for periodic systems but also for disordered cases, as longas the disorder is appropriately restricted, i.e. hyperuniform. It hasalso recently been demonstrated that high quality factor defect cavitiescan be achieved in planar slab architectures putting to rest anypresumption that disorder necessitates infeasible out-of-planescattering. (Amoah and Florescu, submitted to Phys Rev Lett). The PBGsin these disordered materials are comparable in width to those found inPhCs but are also statistically isotropic. This is highly relevant for aseries of novel photonic functionalities including arbitrary angleemission/absorption such as described in “Photon management intwo-dimensional disordered media,” by Vynck et al., Nature Materials,2012; and free-form wave-guiding “Novel Optical Cavity Modes andWaveguide Geometries in Hyperuniform Disordered Photonic Solids” byFlorescu, Steinhardt, and Torquato in Phys. Rev. B, 2012; and by Man etal. in “Isotropic band gaps and freeform waveguides observed inhyperuniform disordered photonic solids,” Proc. Natl. Acad. Sciences,2013. Waveguides in PhCs are intrinsically not flexible, as the anglesbetween waveguides depend on the lattice type. A conventional waveguidecan be considered as a series of connected defect cavities along a pathof scattering centers. In a hyperuniform disordered point pattern such apath would naturally be non-straight. However, even in this case thewaveguide is restricted by the pre-defined template.

Instead of defining a PBG structure first and then designing waveguidesaccordingly we define the path of the waveguide first and then built thestructure around it according to a protocol. This is a bottom-upstrategy. Essentially the question is asked: “If a free-form line in aplane is drawn, what would be a good arrangement of dielectric that ismost like a photonic crystal?” For planar slab architectures, for whichsignificant care about vertical losses has to be taken as compared to2D-only considerations, a connected trivalent network is advantageous toboth the in-plane and vertical confinement of TE radiation. Such adisordered analogue to a photonic crystal can be created by applying aVoronoi method to a distribution of points. Uniformity in the pointdistribution is crucial in order to minimize accidentally-localizedmodes which are promoted into the photonic band gap topologically. Thus,if the right configuration of points around a waveguide is found, asmooth path can be made for the radiation to follow.

FIG. 10 illustrates a schematic of ordering Approaches #1 and #2.Approach #1 indicated by the two “X” marks and triangle labelled “1.” Wefind equally-spaced points on even lines, while on odd lines (e.g. line+1), we find points at half the period while only keep every secondpoint (triangle labelled 1, colored red in associated publication). InApproach #2 (labelled 2 in the Figure and shown in green in associatedpublication), we find equally-spaced points on line 0. We then find thecenter points in-between and translate them to the closest position onthe next line (triangle labelled 2, shown in green in the associatedpublication). Approach #3 is a fusion of Approaches #1 and #2 where oneven lines we find the points by equal spacing and on odd lines bystaggering.

FIG. 11 illustrates a point distribution of the fixed points for a bendin which the points are arranged according to Approach #1, #2, and #3,respectively. Two regular triangular-lattice periodic crystallinesections (with straight boundaries as shown in grey in FIG. 11 and shownas green and red in associated journal article) are connected by bentsections (shown in black in FIG. 11 and as blue in associated journalarticle) where the points are arranged according to Approach #1, #2, and#3, respectively. FIG. 11 thus shows how to distribute the points. Thisfigure shows points distributed as a subsection of a triangular crystaland the parallel lines that are crystal planes parallel to the M highsymmetry direction. One may consider the trivial statement that astraight line is essentially a circular curve at infinite radius. Thenthe crystal planes are just the off-set curves to this infinite circle.This suggests that the scattering centers around our bend waveguideshould be arranged on the off-set curves. This is similar to yetdifferent from the curvilinear lattice approach described by Zarbakhshet al.'s “Arbitrary angle waveguiding applications of two-dimensionalcurvilinear-lattice photonic crystals,” Appl. Phys. Lett., 2004. We haveconsidered two methods by which the triangular lattice can be created byarranging points on the off-set curves, and a third which is acompromise between the first two.

Approach #1: If we consider line 0, we can consider the points to beequally spaced on the line with pitch 1. We can consider line +1 to beline 0 translated by (√3)/2 upward and shifted right (or left) by 0.5.In the case of a straight line, this is also equal to saying that wefound 2N+1 equally spaced points on line +1, and only kept every secondpoint.

Approach #2: Alternatively we can consider that the lattice was built bystaggering the points, i.e. we found the mid-point between points online 0 and found the infinitesimal point on line +1 that is closest tothe mid-point. Then for line +2, we find the closest position to themid-points of line +1, etc.

The strength of Approach #1 is that the points will be distributedrather uniformly in terms of local density; however there is aconsiderable issue with this method. Around the bends, the point patternhas a tendency to transition from an arrangement similar to thetriangular lattice to an arrangement more resembling the square lattice,which is seen in the first example of FIG. 11, FIG. 11A. Acharacteristic loss of staggering of the points is observed for much ofthe curvature. We found this to result in significant topologicallocalization of the electromagnetic radiation, which is expected fromlattice mismatching. For Approach #2 illustrated in FIG. 11B, theproblem is that the distribution becomes too sparse on the convex sideof a bend and too dense on the concave side, leading to local band gapmismatch.

Approach #3: In our final method, we find a compromise between Approach#1 and Approach #2. On even lines we find equally spaced point accordingto Approach #1 and on the next odd line we determine the points bystaggering according to Approach #2.

Hyperuniformity is only well-defined for a statistically isotropic pointdistribution. The integration of a fixed set of points thus breaks thetraditional definition of hyperuniformity. Certain solutions to thetight-packing problem and certain repulsive potential optimizationmethods also produce hyperuniform distributions, as described in “Localdensity fluctuations, hyperuniformity, and order metrics” by Torquatoand Stillinger, Phys Rev E, 2003, and by “Classical disordered groundstates: Super-ideal gases and stealth and equi-luminous materials,” byBatten, Stillinger, and Torquato, Torquato in Journal of Applied Physics(2008). By applying a repulsive potential between N points in a square(√N)×(√N) box with periodic boundary conditions, we obtain a uniformdistribution similar to a χ=0.5 stealthy hyperuniform one. We term thisnear-hyperuniform. Such a simple direct space correlation method makesit easy to define the points around the waveguide as fixed, i.e. notaffected by the sorting algorithm. This capability of embedding a set ofordered designs into a disordered background optical insulator is veryuseful. Complex optical circuits, with multiple waveguides and devicesof different symmetries can be created in the same continuous dielectricsystem, thus reducing input and output coupling issues betweencomponents.

FIG. 12 shows the waveguide modes of a triangular photonic crystal ofhexagons, i.e. a honeycomb structure. The even waveguide modes are shownin black (which appears red in the associated journal publication) andthe odd modes in grey (which appears green in the associated journalpublication). For the straight reference waveguide we chose symmetryconditions such that only even waveguide modes are excited andcontribute to transmission. Low-loss waveguiding relates to the conceptof guided modes. For a suspended dielectric slab in a homogeneousambient dielectric there are guided modes, modes below the light line(which is the dispersion of the ambient homogeneous dielectric, hereair) which cannot couple to the unguided radiating modes above the lightline. In photonic slabs, while there exists no true band gap, theexistence of “pseudo-band-gaps” enables low-loss waveguiding and high Qcavities, as described in “High-Q photonic nanocavity in atwo-dimensional photonic crystal” by Akahane et al., Nature, 2003. Wecall the area of low loss as marked in FIG. 13 the low-loss transmissionwindow.

FIG. 12: Dispersion relation of the waveguide modes of a triangularlattice of hexagons (honeycomb) W1 waveguide is shown on the left sideof the FIG. 12. The corresponding transmission spectrum is shown on theright of the figure. Horizontal dashed lines outline stop bands anddiagonal dashed line is the light line.

FIG. 13: Transmission at successive virtual monitors along a long (80a)regular honeycomb waveguide. Low-loss waveguiding is observed for theindex-guided region.

FIG. 14 illustrates the disordered honeycomb structures with embeddedwaveguides. FIG. 14: Plan-view cross section of waveguides curvedaccording the equations specified for Designs A, B, and C in thexy-plane. In each case, the design structures are each composed of tworegular, periodic photonic crystal sections and a bent crystal sectionconnecting the two periodic photonic crystal sections. The bent crystalsections are based on the curves defined by the associated equations forDesigns A, B, and C, respectively, and the adjacent layers areconstructed on the off-set curves using Approach #3. The waveguide andadjacent layers are embedded in a near hyperuniformbackground-insulating network.

Design A features a waveguide following the curve, x∈{−15<x<15}, y=3(√3)tan h (x/5).

Design B features a waveguide that follows a 90 degree bend along acircular curve given by θ∈{0, π/2}, r=4(√3), x=r sin θ−r, and y=r sinθ+r.

Design C features a waveguide that follows the following curve:x∈{−15<x<15}, y=(15/π)(cos(π×/15)+1)/2.

A commercial-grade simulator based on the finite-difference time-domainmethod was used to perform the calculations. A domain of 40a×40a isdefined. The total number of points is set to N_(total)=1600 in order toobtain unit density. For all designs we chose the unit length a to be460 nm. In each case we place two triangular crystals of size(12a)(13)[(√3)/2)]a either at the left and right domain edge (Design Aand Design C) or at the left and top (rotated by 90 degrees) (Design B).Curved sections are created by defining a path between the central rowof the crystals according the respective function and by decorating thepath and 7 layers of offset curves either side according to Approach #3.Together the crystal and curved section are declared a set of fixedpoints N_(fixed). The number of movable points is thusN_(movable)=N_(total)−N_(fixed). N_(movable) points are now distributedrandomly in the domain. We apply a repulsive r⁻⁴ potential with respectto all points under periodic boundary conditions, but only allow themovable points to uniformize.

We apply to the point pattern the network protocol described in thefollowing two references: M. Florescu, S. Torquato, and P. J.Steinhardt, “Designer disordered materials with large complete photonicband gaps,” Proc. Natl. Acad. Sci. U.S.A., vol. 106, no. 49, pp.20658-20663, 2009 and M. Florescu, S. Torquato, and P. J. Steinhardt,“Complete band gaps in two-dimensional photonic quasicrystals,” Phys.Rev. B—Condens. Matter Mater. Phys., vol. 80, 2009. The wall width isset to 0.4a (184 nm) and the slab height to 0.478a (220 nm). The cellsalong the waveguide path are filled with dielectric. Input and outputstrip waveguides of width, (√3)/2a(398 nm) are placed at the beginningand end. The structure is placed in a FDTD domain of 45a×45a×3.65a. Amode source is used to launch the fundamental (even) TE mode of thestrip input waveguide.

FIG. 15 shows the spectral transmission as a function of wavelength forour three designs. We observe significant transmission up to around 70%compared to 80% obtained for the straight waveguide, i.e. 13% loss, inthe low loss transmission window. Some resonance anomalies associatedwith these curved waveguides are observed at longer wavelengths. Atthese wavelengths the dispersion of the straight waveguide flattens outand thus the group velocity is much slower. This substantially slowedgroup velocity could in some applications be used to advantage, while inother applications it might be preferred to eliminate the dispersion viafurther optimization in the vicinity of the waveguide. Using thesestructures as a starting point for further numerical optimizationswell-known to individuals skilled in the art, transmission spectraclosely approaching that for the straight waveguides is expected.

FIG. 15: Transmission spectra for an ordinary straight honeycombphotonic crystal waveguide (black), a straight waveguide with 7triangular lattice layers embedded in a near-hyperuniform background(red) and a waveguide bent at a 90 degree angle with a radius r=4(√3).From top to bottom in this figure are the transmission spectracorresponding to 90 degree bends described in Designs A (labelled hereas tan h), B (labelled here as 90 degree), and C (labelled here as cos)respectively, embedded in a near-hyperuniform background. Thegrey-shaded region (blue-shaded in associated journal publication) isthe low-loss window for the straight waveguide. Further improvements areexpected to accrue to the transmission spectra of the bent waveguidesupon application of further numerical optimizations.

In summary, we have proposed and demonstrated a novel design strategyfor non-straight waveguides in disordered honeycomb type structures. Aparticularly interesting result is that we connected two triangularlattices M-direction W1 waveguides around a 90° bend, an angle notnaturally provided in the case of the regular, periodic triangularcrystal. Our initial designs have shown that transmission is possible inthe low loss transmission window of the regular photonic crystal. Thisis highly relevant to the field of sub-wavelength structured materialsespecially since we have shown this for 220 nm silicon membranetechnology around 1.6 μm. These length scales are not only relevant forphotonics applications, but also for phononic, phoxonic andopto-mechanical applications where simultaneous localization and guidingof light and sound waves is achieved, such as described in “PhotonicBand Gap Optomechanical Crystal Cavity,” by Safavi-Naeini et al, Phys.Rev. Lett., 2010. Structures based on this approach are promisingtemplates which, when used as starting points for further optimization,can lead to very high performing integrated optical microcircuits,providing a generalized design platform for compact, PBG-based PICs.

Expanded control over the flow of light can have a great impact onall-optical switching as referenced for example in “Resonancefluorescence in photonic band gap waveguide architectures: Engineeringthe vacuum for all-optical switching,” by Florescu and John, Phys Rev A,2004; implementations of linear-optical quantum information processorsas described for example in “Exploiting the Quantum Zeno effect to beatphoton loss in linear optical quantum information processors,” bySpedalieri et al., Optics Communications, 2005; single-photon sources,optical computing, and lab-on-chip metrology.

The processes explained above are described in terms of computersoftware and hardware. The techniques described may constitutemachine-executable instructions embodied within a tangible ornon-transitory machine (e.g., computer) readable storage medium, thatwhen executed by a machine will cause the machine to perform theoperations described. Additionally, the processes may be embodied withinhardware, such as an application specific integrated circuit (“ASIC”) orotherwise.

A tangible non-transitory machine-readable storage medium includes anymechanism that provides (i.e., stores) information in a form accessibleby a machine (e.g., a computer, network device, personal digitalassistant, manufacturing tool, any device with a set of one or moreprocessors, etc.). For example, a machine-readable storage mediumincludes recordable/non-recordable media (e.g., read only memory (ROM),random access memory (RAM), magnetic disk storage media, optical storagemedia, flash memory devices, etc.).

The above description of illustrated embodiments of the invention,including what is described in the Abstract, is not intended to beexhaustive or to limit the invention to the precise forms disclosed.While specific embodiments of, and examples for, the invention aredescribed herein for illustrative purposes, various modifications arepossible within the scope of the invention, as those skilled in therelevant art will recognize.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification. Rather, the scope of the invention is tobe determined entirely by the following claims, which are to beconstrued in accordance with established doctrines of claiminterpretation.

What is claimed is:
 1. An optical modulator comprising: a waveguideconfigured to guide an optical signal; a Hyperuniform Disordered Solid(“HUDS”) structure formed by walled cells organized in a lattice,wherein the lattice includes a semiconductor material, and wherein eachof the walled cells surrounds a fill material that differs from amaterial that forms the walled cells, and further wherein a first indexof refraction of the fill material and a second index of refraction ofthe material that forms the walled cells have an oppositely-signeddependence of index of refraction on temperature; a first electricalcontact coupled to a first doping region within the semiconductormaterial; a second electrical contact coupled to a second doping regionwithin the semiconductor material; and a resonant structure, wherein thefirst and second doping regions are disposed to modulate an index ofrefraction of the resonant structure in response to a modulation signalacross the first and second electrical contacts, and wherein modulatingthe index of refraction of the resonant structure modulates the opticalsignal propagating through the waveguide.
 2. The optical modulator ofclaim 1, wherein the first doping region has a first polarity that isopposite a second polarity of the second doping region.
 3. The opticalmodulator of claim 1, wherein the lattice, the waveguide, and theresonant structure are all defined by a contiguous structure.
 4. Theoptical modulator of claim 1, wherein the semiconductor materialincludes silicon.
 5. The optical modulator of claim 1, wherein theresonant structure is defined by an enlarged hole in the lattice that islarger than a hole size of any one of the walled cells in a defect-freeportion of the lattice.
 6. The optical modulator of claim 1, wherein theresonant structure includes at least one of the walled cells of thelattice being a filled or partially-filled cell.
 7. The opticalmodulator of claim 1 further comprising an adjusted interface disposedbetween the HUDS structure and the waveguide, wherein boundaries of thewaveguide enclose walled interface cells that contact the waveguide, thewalled interface cells included in the adjusted interface.
 8. Theoptical modulator of claim 1, wherein the semiconductor materialincludes gallium.
 9. An optical transceiver comprising: an input port toreceive an incoming optical communication signal; an output port totransmit an outgoing optical communication signal; and a photonicintegrated circuit (“PIC”) optically coupled between the input port andthe output port, the PIC comprising: a controller; a waveguideconfigured to guide the incoming optical communication signal; aHyperuniform Disordered Solid (“HUDS”) structure formed by walled cellsorganized in a lattice, wherein the lattice includes a semiconductormaterial, and wherein each of the walled cells surrounds a fill materialthat differs from a material that forms the walled cells, and furtherwherein a first index of refraction of the fill material and a secondindex of refraction of the material that forms the walled cells have anoppositely-signed dependence of index of refraction on temperature; afirst electrical contact coupled to a first doping region within thesemiconductor material; a second electrical contact coupled to a seconddoping region within the semiconductor material; and a resonantstructure, wherein the first and second doping regions are disposed tomodulate the outgoing optical communication signal by modulating anindex of refraction of the resonant structure in response to amodulation signal across the first and second electrical contacts, themodulation signal received from the controller.
 10. The opticaltransceiver of claim 9, wherein the lattice, the waveguide, and theresonant structure are all defined by a contiguous structure.
 11. Theoptical transceiver of claim 9, wherein the first doping region has afirst polarity that is opposite a second polarity of the second dopingregion.
 12. The optical modulator of claim 9, wherein the semiconductormaterial includes silicon.
 13. An optical modulator comprising: awaveguide configured to guide an optical signal; a HyperuniformDisordered Solid (“HUDS”) structure formed by walled cells organized ina lattice, wherein the lattice includes a semiconductor material; afirst electrical contact coupled to a first doping region within thesemiconductor material; a second electrical contact coupled to a seconddoping region within the semiconductor material; a resonant structure,wherein the first and second doping regions are disposed to modulate anindex of refraction of the resonant structure in response to amodulation signal across the first and second electrical contacts, andwherein modulating the index of refraction of the resonant structuremodulates the optical signal propagating through the waveguide; and anadjusted interface disposed between the HUDS structure and thewaveguide, wherein boundaries of the waveguide enclose walled interfacecells that contact the waveguide, the walled interface cells included inthe adjusted interface.
 14. The optical modulator of claim 13, whereinthe lattice, the waveguide, and the resonant structure are all definedby a contiguous structure.
 15. The optical modulator of claim 13,wherein the first doping region has a first polarity that is opposite asecond polarity of the second doping region.
 16. The optical modulatorof claim 13, wherein the semiconductor material includes gallium. 17.The optical modulator of claim 13, wherein the semiconductor materialincludes silicon.
 18. The optical modulator of claim 13, wherein each ofthe walled cells includes an air hole enclosed by walls.
 19. The opticalmodulator of claim 13, wherein the resonant structure is defined by anenlarged hole in the lattice that is larger than a hole size of any oneof the walled cells in a defect-free portion of the lattice.
 20. Theoptical modulator of claim 13, wherein the resonant structure includesat least one of the walled cells of the lattice being a filled orpartially-filled cell.
 21. The optical modulator of claim 13, whereinthe lattice is formed of a semiconductor material, and wherein thewalled cells enclose voids in the semiconductor material.
 22. Theoptical modulator of claim 21, wherein the voids are filled with air.23. The optical modulator of claim 21, wherein the voids are a vacuum.24. The optical modulator of claim 21, wherein the voids are filled withan oxide.
 25. The optical modulator of claim 21, wherein the voids arefilled with a nitride.